Two-phase and three-phase relative permeability of unconventional Niobrara chalk using integrated core and 3D image rock physics

Transcription

1 Two-phase and three-phase relative permeability of unconventional Niobrara chalk using integrated core and 3D image rock physics Alan P. Byrnes*, Whiting Oil & Gas Corporation Shawn Zhang, DigiM Solution LLC Lyn Canter, Whiting Oil & Gas Corporation Mark D. Sonnenfeld, Whiting Oil & Gas Corporation 1

2 Overview Key questions Methodology - Findings Geology Methodologies (critical to low-k) Representative Elementary Volume (REV) Permeability Porosity - Capillary Pressure Relative Permeability Bound Water Conclusions 2

3 Overview Key Questions for reservoir characterization and flow modeling What is the permeability (K) and porosity (φ) relationship (K-φ)? What are saturations and capillary pressure (Pc) relationships (e.g., Pc-φ, Pc-K, Threshold entry Pc, Brooks-Corey λ)? What are the 2-Phase (G-O, O-W) and 3-Phase (G-O-W) relative permeability (Krg, Krog, Krow, Krw, Krogw) relationships? What is a robust Core Analysis-Image Based Rock Physics (CA-IBRP) integrated workflow? Methodology Measure φ, K, Pc, Kr on using CA and DRP for representative Niobrara (NBRR) Correlate/calibrate CA IBRP Evaluate Representative Elementary Volume (REV) or statistical REV (SREV) for each property Key Findings Developed an integrated CA-IBRP cross-validation workflow CA and DRP give similar K-φ, Pc, Kr with proper stress correction DRP provides complete Krw and Kro curves not easily measured by CA DRP provides 3-Phase Kro curves never measured by CA Bound water influences K in rocks with K < md 3

4 Niobrara in DJ Basin and Vertical Facies Profile Interior Cretaceous Seaway deeptimemaps.com Highstands/Lowstands - Vertical succession of chalks and marlstones 4

5 Mineralogy & Diagenesis SEM Niobrara chalk; Sherman Co., KS, 1,000 ft, φ = 0.411, Kik = 2 md (after Byrnes et al, 2005) 5

6 Methodologies Core Analysis Methodology Data from three major labs Dean-Stark/Soxhlet cleaning Porosity Boyle s Law Helium porosity core and crushed Pore volume compressibility measured on select core plugs Normalized to 2,000 psi Net Confining Stress (NCS) Permeability Core plug Klinkenberg (@NCS) & crushed rock (GRI) Permeability (Kik) stress dependence measured on select core plugs Normalized to 2,000 psi NCS Capillary Pressure Mercury intrusion (MICP) MICP curves measured under variable NCS as a function of entry pressure Cores with Kik< ~800 nd significantly affected by Hg-NCS (Important!!) Reference permeability of MICP sample adjusted for Hg-NCS Relative Permeability As-received and cleaned crushed rock Sl computed from A-R Kg/cleaned Kg 6

7 Steady-State IBRP Relative Permeability Workflow Digital Porosimetry Image Processing CFD: Permeability

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9 Image Processing Methodology 1 µm 2 µm 5 µm Artificial intelligence based image segmentation (AIBIS) Two key issues pore backs & residual oil (oil vs kerogen) Train subset on grey scale and statistical measures AIBIS correctly segments OM (C) Segmentation on full 2D field (E) Segmentation on full 3D image stack (F)

10 IBRP Permeability Methodology Permeability measured/computed/modeled using computational fluid dynamic (CFD) simulation module from the DigiM Image to Simulation (I2S) cloud computing platform Connected 3D pore structure from the FIB-SEM image volume is reconstructed from the original imaging resolution not reduced to a pore network model (PNM) and not LB. Finite volume spatial discretization is built directly on voxels of the segmented 3D imaging data. Navier-Stokes equations solved with an implicit pressure/explicit momentum scheme (Versteeg and Malalasekera, 2007): u = 0 p = µ 2 u (u )u + f Using pressure and velocity fields solution, Darcy s law used for permeability in each direction (n): k n = u n µ x/ p (u = fluid velocity vector, p =pressure, µ= dynamic viscosity, f = body force vector = 0) Scalar Permeability: k mag = k 2 e0+k 2 e1+k 2 e2 10

11 IBRP Capillary Pressure chalk with φ = 0.156, Kk= md 10 µm Method derived from Hilpert & Miller (2001) Successive invasion of FIB-SEM pore volume with spheres of defined diameter (equivalent to pressure through Washburn (1921) relation: D = 4σCosθ/Pc) 11

12 IBRP Drainage Relative Permeability 10 µm Series of saturation states achieved by drainage Pc Permeabilities to the non-wetting (e.g., Ko, Kg) and wetting (Kw) phase are computed for their quasi-static distribution (single-phase stationary in CA). Relative permeability computed by reference to absolute permeability 12

13 IBRP 3-Phase Relative Permeability Similar in process to 2- phase Kr Series of saturation states achieved by drainage Pc Oil partially displaces water Gas partially displaces oil Mirrors solution gas drive Permeabilities to each phase is computed for their quasi-static distribution. Relative permeability computed by reference to absolute permeability 13

14 Representative Elementary Volume Chalks are Heterogeneous 1) Peloids 2) Porous matrix 3) Clay-rich matrix φ = 14.9% φ = 12.8% φ = 12.9% Vertical heterogeneity at many scales 14

15 Porosity Sampling & REV FIB-SEM samples span φ but limited # samples do not exhibit exact same distribution as core/logs FIB/SEM sample with φ = 16.3% and sample dimensions of 8 3 µm 3 is φrev at 0.6 fraction. 15

16 Representative Elementary Volume Properties exhibit scale-dependence at micro (SEM), macro (core) and field scales and spatially (horizontal and vertical) Both Core and IBRP challenged by deterministic REV definition REV varies with property: REV φ <REV k <REV Pc <REV kr Lateral continuity 1x4 km (Horizontal well drainage area) Vertical continuity significantly influenced by mm-scale bedding and lithology no good REVvertical Define properties at an appropriate fine scale and apply within a geocellular model Statistical REVs or SREV Measure/model properties on samples of a sufficient size to be an SREV for that property Practical to assign within a geomodel Do not expect single SREV to reproduce larger-sample properties will reproduce larger sample relationships 16

17 Types of REV Characterization Phase Location/ Property Property can be characterized at REV resolution Property cannot be characterized at REV resolution Location Known Type 1 Type 2 Location Unknown N/A Type 3 To obtain meaningful properties from Image-based rock physics (IBRP)it is required that properties be measured on a REV For coarser-grained samples it is necessary to obtain properties of components and upscale within a model similar to reservoir numerical flow simulation 17

18 Permeability vs Porosity φ, K, Pc Kik-φ trend for Niobrara chalks and marls IBRP=IBRP Kik-φ = CA Kik-φ (Kik = insitu Klinkenberg Permeability) Important: IBRP FIB-SEM samples do not have microfractures High correlation of IBRP-CA confirms CA φ, K, φ(ncs), K(NCS) not influenced by microfractures IBRP and CA Kik-φ were developed completely independently 18

19 Permeability vs Porosity φ, K, Pc Kik-φ trend for Niobrara chalks and marls Variance in Kik-φ trends results from combinations of SREVs in a single sample samples are actually pseudo-samples combining many layers If samples contain thin beds of very high porosity Kik-φ can deviate from powerlaw type trend. 19

20 CA & DRP Capillary Pressure MICP under too much stress not real Dte λ Core (high Pconf) IBRP (Pconf= 0) 20

21 Pore Throat Size Distribution Image Resolution 5-20 nm Sample Size µm Use Dte-K and λ-k relationships 10 nm (0.01 µm) image resolution φ>8%: pore throats of 95% PV φ=6%: pore throats of 80% PV φ<6%: need 5 nm resolution but may compromise REV 21

22 Importance of Relative Permeability to Recovery Using accurate relative permeability relationships is critical to accurately predicting gas and oil production For Niobrara standard Corey parameters over-predict early-time performance and GOR. RMAG DWLS Fall Syposium Sept 27, 2017

23 Relative Permeability - Simple Systems Straight capillaries Equal radius No wetting saturation (Swi=0) kro+krw=1 Complex pore bodypore throat architecture Non-uniform fluid distribution Decisions at junctions Non-equal pore size distribution No wetting saturation (Swi=0) kro+krw 1

24 Niobrara Gas Relative Permeability Weatherford and TerraTek As- Received effective gas permeability measurements generally exhibit Krgvalues consistent with a Corey exponent for gas, eg= where; Krg= (Sg/(1-Swc)) eg ; Swc=0.1 Krg=Keg/K air-routine 24

25 Digital Rock Physics Relative Permeability So=88% kro=90% krw=0.0001% So=63% kro=19% krw=0.65% Niobrara φ = 9.4% k = 1.59 µd So=50% kro=6.3% krw=3.1% So=26% kro=0.3% krw=21% kro= (So/(1-Swc)) 4.7 Swc= 0.10 krw= ((Sw-Swc)/(1-Swc)) 4 micron So=19% kro=0.07% krw=31% Fluid saturation (oil-green, water-blue) is computed by digital porosimetry. Permeability at each saturation is computed with computational fluid dynamics solving Navier- Stokes equations. Relative permeability referenced to Kabs krw not corrected for kw/kik

26 2-Phase CA-Kr vs IBRP-Kr Relative Permeability In low-k rocks, solution gas drive, drainage Kr dominates (except early-time hyd frac face) IBRP-Krg = CA-Krg completely independent measures IBRP provides complete curves φ = 9.4%-31.4%; Kik = 1.6 µd-343 µd IBRP Corey parameters Snwc = Sgc = Soc = 0, Swc=0.1 enw = eg = eo = 4.7 (black enw=3.7 & 5.7) ew = 4 Similar Kro and Krw for wide range of K-φ No systematic shift in eo or ew = = = =

27 Three-Phase Relative Permeability Sg=19% krg=0.07% So=44% kro=0.5% Sw=37% krw=0.6% 3-Phase Isoperm s Sg=50% krg=6.3% So=38% kro=1.7% When 3 phases are present in a drainage cycle: micron Sw=12% krw=0.0001% Gas (red) occupies largest pores and krgis dependent only on Sg Water (blue) occupies smallest pores and krw is dependent only on Sw Oil (green) occupies intermediate pores and krois more complex function of Sg, So, and Sw

28 IBRP 3-Phase Relative Permeability Krw= f(sw) ew=4 Corey eogw=4.7 CA 3-P Krogw almost impossible to measure on low-k and no CA data exist IBRP 3-P Krogw modeling similar to 2-P where Kro is computed for quasi-static So 3-P Krogw Corey eogw = P Krogw Stone I eogw = 9.0 Krg= f(sg) eg=4.7 Stone I eogw=9 = = : = : =

29 Bound Water vs Permeability Permeability Permeability Permeability Permeability reduction reduction reduction reduction Pore Throat Pore Throat for 1-layer for 1-layer for 3-layer for 3-layer In situ Diameter Diameter Boundwater Boundwater Boundwater Boundwater Sw=0.1 Dte De Dte De (md) (Dte, µm) (De, µm) (fraction) (fraction) (fraction) (fraction) Water Types 1. Free (capillary force<<viscous force) 2. Capillary-bound (capillary force>>viscous force) 3. External surface electrostatic-bound (adsorbed, ~2-molecules thick) 4. Internal surface electrostatic-bound (between clay sheets, =f(salinity)) 5. Structural (ionic-covalent bond force dominate) Focusing only on water on pore wall surface and ignoring water retained in very small pores by Pc Bound water alone exerts minor influence on K for K>0.01 md Bound water exerts significant influence on K for K < md 29

30 Conclusions Demonstrated an integrated workflow for cross-validating CA-DRP in low-k rock Both core plugs and FIB/SEM samples are SREVs in Niobrara CA and DRP give similar K-φ, Pc, Kr with proper stress correction Just as with CA, influence of NCS must be considered for DRP properties For K< ~800 nd, Pc curves are strongly influenced by Hg-induced stress DRP indicates Niobrara core K-φ, K-NCS and φ-ncs not influenced by micro-cracks DRP provides complete Krw and Kro curves not easily measured by CA DRP provides 3-Phase Kro curves (never measured by CA?) Bound water influences K in rocks with K < md Important to note that results in this study are specific to Niobrara rocks (Type 1) - other methodologies are required for samples with larger REVs (Type 2 & 3) Properties measured in this study have been utilized in flow modeling to support exploration, completion, and production management decisions 30

31 Thank You for Your Time Questions? Alan P. Byrnes*, Whiting Oil & Gas Corporation Shawn Zhang, DigiM Solution LLC Lyn Canter, Whiting Oil & Gas Corporation Mark D. Sonnenfeld, Whiting Oil & Gas Corporation DWLS Jan 16,